Effect of payload size on mean response time when message segmentations occur using $\rm{M}^{\rm X}/\rm{G}/1$ queueing model

TL;DR

This paper introduces an $ m{M}^{ m X}/ m{G}/1$ queueing model to analyze how payload size affects mean response time during message segmentation, providing a closed-form solution and numerical insights.

Contribution

It develops a novel queueing model for segmented message arrivals and derives a closed-form expression for mean response time considering payload size and message distribution.

Findings

Mean response time increases convexly with payload size at higher arrival rates.

The model accurately predicts response times in web object delivery scenarios.

Numerical results highlight the impact of payload size on response time convexity.

Abstract

This paper proposes the $\rm{M}^{\rm X}/\rm{G}/1$ queueing model to represent arrivals of segmented packets when message segmentations occur. This queueing model enables us to derive the closed form of mean response time, given payload size, message size distribution and message arrival rate. From a numerical result, we show that the mean response time is more convex in payload sizes if message arrival rate is larger in a scenario where Web objects are delivered over a physical link.